Watch out: This one is different! A rectangular box with a square base has surface area of 30 ft.2. Find a formula for the volume of the box as a function of the side length of the base x. Problem 5.

Q: 1. 1400 cm² of material is available to create a box with a square base, and a closed top. Draw a…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: A 900 ft.³ pool is to be built with the square bottom of side length X. The sides are built with…

A: Given volume of the pool as 900 cubic foot with square bottom of side x.   Also given that the cost…

Q: This problem illustrates a typical approach for creating a model. Use lower case letters. We want to…

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Q: 5. A square-based pyramid has a height that is twice its base length. a) Determine an equation to…

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Q: Problem 2. A cylinder has a surface area of 1000 in.. Find a formula for the volume as a function of…

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Q: Situation C: A 1-gallon paint can with a height of 7.5 inches contains about 250 cubic inches of…

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Q: The mass of a spherical solid is inversely proportional as its density and the cube of its…

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Q: A box with a square base and open top must have a volume of 296352 cm³. We wish to find the…

A: It is provided that the base of the box is square and top of the box is open. The volumeV of the box…

Q: A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus the diameter of the…

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Q: 8. If the volume of the cuboid 350 cubic cm, fength = 10 cm ànd breadth = 5 cm. Then %3D %3D find…

A: We have to find the height of the cuboid where the volume, length and breadth are given.

Q: Problem 2. A rectangular box without a lid is to be made from 16 cm² of plastic. Find the maximum…

A: We can solve the given problem by using the partial derivatives.

Q: the volume of a tetrahedron ( a pyramid where each side is an equilateral triangle) is given by…

A: Let us assume the original value of the length of the side is 10 cm and as per the question, the…

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.